arXiv subjects

A. J. Webster

Publications and source records attributed to A. J. Webster.

11 recordsLinked to original sources

arXiv2021

When can relative risks provide causal estimates?

It is emphasised that for epidemiological studies where disease incidence is rare, results from conventional proportional hazards models can often correctly estimate causal associations. The well-known "backdoor criteria" from causal-inference is applied to the common epidemiological study of rare diseases with a proportional hazards model, providing an example of when and how estimates from conventional proportional hazards studies can be used. A similar study with the "frontdoor criteria", that allows studies with unmeasured confounders, finds similar results to conventional mediation analysis with measured confounders. Reasons for this are discussed.

stat.ME↗

arXiv2019

Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

Complex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. Multi-stage models provide a simple but very general mathematical framework for studying the failure of complex systems, or equivalently, the onset of disease. They include the Armitage Doll multi-stage cancer model as a particular case, and have potential to provide new insights into how failures and disease, arise and progress. A method described by E.T. Jaynes is developed to provide an analytical solution for a large class of these models, and highlights connections between the convolution of Laplace transforms, sums of random variables, and Schwinger/Feynman parameterisations. Examples include: exact solutions to the Armitage-Doll model, the sum of Gamma-distributed variables with integer-valued shape parameters, a clonal-growth cancer model, and a model for cascading disasters. Applications and limitations of the approach are discussed in the context of recent cancer research. The model is sufficiently general to be used in many contexts, such as engineering, project management, disease progression, and disaster risk for example, allowing the estimation of failure rates in complex systems and projects. The intended result is a mathematical toolkit for applying multi-stage models to the study of failure rates in complex systems and to the onset of disease, cancer in particular.

stat.ME↗

arXiv2014

Distinguishing Cause from Correlation in Tokamak Experiments to Trigger Edge Localised Plasma Instabilities

The generic question is considered: How can we determine the probability of an otherwise quasirandom event, having been triggered by an external influence? A specific problem is the quantification of the success of techniques to trigger, and hence control, edge-localised plasma instabilities (ELMs) in magnetically confined fusion (MCF) experiments. The development of such techniques is essential to ensure tolerable heat loads on components in large MCF fusion devices, and is necessary for their development into economically successful power plants. Bayesian probability theory is used to rigorously formulate the problem and to provide a formal solution. Accurate but pragmatic methods are developed to estimate triggering probabilities, and are illustrated with experimental data. These allow results from experiments to be quantitatively assessed, and rigorously quantified conclusions to be formed. Example applications include assessing whether triggering of ELMs is a statistical or deterministic process, and the establishment of thresholds to ensure that ELMs are reliably triggered.

physics.plasm-ph↗

arXiv2014

The unintended influence of control systems on edge-plasma transport and stability in the Joint European Torus

A unique experiment in the Joint European Torus (JET) consecutively produced 120 almost identical plasma pulses, providing two orders of magnitude more data than is usually available. This allows the statistical detection of previously unobservable phenomena such as a sequence of resonant-like waiting times between edge-localised instabilities (ELMs). Here we investigate the causes of this phenomenon. By synchronising data to the 1000s of ELM times and averaging the results, random errors are reduced by a factor of 50, allowing unprecedentedly detailed behaviour to be described. A clear link can then be observed between plasma confinement, ELM occurrence, vertical plasma oscillations, and an otherwise unobservable oscillation in a control coil current that is not usually associated with ELM occurrence. The results suggest a strong and unanticipated edge-plasma dependence on control system behaviour.

physics.plasm-ph↗

arXiv2013

Time-Resonant Tokamak Plasma Edge Instabilities?

For a two week period during the Joint European Torus (JET) 2012 experimental campaign, the same high confinement plasma was repeated 151 times. The dataset was analysed to produce a probability density function (pdf) for the waiting times between edge-localised plasma instabilities ("ELMS"). The result was entirely unexpected. Instead of a smooth single peaked pdf, a succession of 4-5 sharp maxima and minima uniformly separated by 7-8 millisecond intervals was found. Here we explore the causes of this newly observed phenomenon, and conclude that it is either due to a self-organised plasma phenomenon or an interaction between the plasma and a real-time control system. If the maxima are a result of "resonant" frequencies at which ELMs can be triggered more easily, then future ELM control techniques can, and probably will, use them. Either way, these results demand a deeper understanding of the ELMing process.

physics.plasm-ph↗

arXiv2013

Identifying low-dimensional dynamics in Type-I edge-localised-mode processes in JET plasmas

Edge localised mode (ELM) measurements from reproducibly similar plasmas in the Joint European Torus (JET) tokamak, which differ only in their gas puffing rate, are analysed in terms of the pattern in the sequence of inter-ELM time intervals. It is found that the category of ELM defined empirically as Type I - typically more regular, less frequent, and having larger amplitude than other ELM types - embraces substantially different ELMing processes. By quantifying the structure in the sequence of inter-ELM time intervals using delay time plots, we reveal transitions between distinct phase space dynamics, implying transitions between distinct underlying physical processes. The control parameter for these transitions between these different ELMing processes is the gas puffing rate.

physics.plasm-ph↗

arXiv2013

Statistical Characterisation and Classification of Edge Localised Plasma Instabilities

The statistics of edge-localised plasma instabilities (ELMs) in toroidal magnetically confined fusion plasmas are considered. From first principles, standard experimentally motivated assumptions are shown to determine a specific probability distribution for the waiting times between ELMs: the Weibull distribution. This is confirmed empirically by a statistically rigorous comparison with a large data set from the Joint European Torus (JET). The successful characterisation of ELM waiting times enables future work to progress in various ways. Here we present a quantitative classification of ELM types, complementary to phenomenological approaches. It also informs us about the nature of ELMing processes, such as whether they are random or deterministic.

physics.plasm-ph↗

arXiv2009

Magnetohydrodynamic Stability at a Separatrix: Part I

The rapid deposition of energy by Edge Localised Modes (ELMs) onto plasma facing components, is a potentially serious issue for large Tokamaks such as ITER and DEMO. The trigger for ELMs is believed to be the ideal Magnetohydrodynamic Peeling-Ballooning instability, but recent numerical calculations have suggested that a plasma equilibrium with an X-point - as is found in all ITER-like Tokamaks, is stable to the Peeling mode. This contrasts with analytical calculations (G. Laval, R. Pellat, J. S. Soule, Phys Fluids, {\bf 17}, 835, (1974)), that found the Peeling mode to be unstable in cylindrical plasmas with arbitrary cross-sectional shape. However the analytical calculation only applies to a Tokamak plasma in a cylindrical approximation. Here, we re-examine the assumptions made in cylindrical geometry calculations, and generalise the calculation to an arbitrary Tokamak geometry at marginal stability. The resulting equations solely describe the Peeling mode, and are not complicated by coupling to the ballooning mode, for example. We find that stability is determined by the value of a single parameter $Δ'$ that is the poloidal average of the normalised jump in the radial derivative of the perturbed magnetic field's normal component. We also find that near a separatrix it is possible for the energy principle's $δW$ to be negative (that is usually taken to indicate that the mode is unstable, as in the cylindrical theory), but the growth rate to be arbitrarily small.

physics.plasm-ph↗

arXiv2009

Magnetohydrodynamic Stability at a Separatrix: Part II

In the first part to this paper\cite{part1} it was shown how a simple Magnetohydrodynamic model could be used to determine the stability of a Tokamak plasma's edge to a Peeling (External Kink) mode. Stability was found to be determined by the value of $Δ'$, a normalised measure of the discontinuity in the radial derivative of the radial perturbation to the magnetic field at the plasma-vacuum interface. Here we calculate $Δ'$, but in a way that avoids the numerical divergences that can arise near a separatrice's X-point. This is accomplished by showing how the method of conformal transformations may be generalised to allow their application to systems with a non-zero boundary condition, and using the technique to obtain analytic expressions for both the vacuum energy and $Δ'$. A conformal transformation is used again to obtain an equilibrium vacuum field surrounding a plasma with a separatrix. This allows the subsequent evaluation of the vacuum energy and $Δ'$. For a plasma-vacuum boundary that approximates a separatrix, the growth rate $γ$ normalised by the Aflven frequency $γ_A$ is then found to have $\ln(γ/γ_A)=-{1/2} \ln (q'/q)$. Consequences for Peeling mode stability are discussed.

physics.plasm-ph↗

arXiv2001

Osmotic Stabilisation of Concentrated Emulsions and Foams

In the absence of coalescence, coarsening of emulsions (and foams) is controlled by molecular diffusion of dispersed phase between droplets/bubbles. Studies of dilute emulsions have shown how the osmotic pressure of a trapped species within droplets can ``osmotically stabilise'' the emulsion. Webster and Cates (Langmuir, 1998, 14, 2068-2079) gave rigorous criteria for osmotic stabilisation of mono- and polydisperse emulsions, in the dilute regime. We consider here whether analogous criteria exist for the osmotic stabilisation of mono- and polydisperse concentrated emulsions and foams, and suggest that the pressure differences driving coarsening are small compared to the mean Laplace pressure. An exact calculation confirms this for a monodisperse 2D model, finding a bubble's pressure as P_i = P + Pi + P_i^G, with P, Pi the atmospheric and osmotic pressures, and P_i^G a ``geometric pressure'' that reduces to the Laplace pressure only for a spherical bubble. For Princen's 2D emulsion model, P_i^G is only 5% larger in the dry limit than the dilute limit. We conclude that osmotic stabilisation of dense systems typically requires a pressure of trapped molecules in each droplet that is comparable to the Laplace pressures the same droplets would have if spherical, as opposed to the much larger Laplace pressures present in the system. We study coarsening of foams and concentrated emulsions when there is insufficient of the trapped species present. Rate-limiting mechanisms are considered, their applicability and associated droplet growth rates discussed. In a concentrated foam or emulsion, a finite yield threshold for droplet rearrangement may be enough to prevent coarsening of the remainder.

cond-mat.soft↗

arXiv1998

Stabilisation of Emulsions by Trapped Species

We consider an emulsion whose droplets contain a trapped species (insoluble in the continuous phase), and study the emulsion's stability against coarsening via Lifshitz-Slyozov dynamics (Ostwald Ripening). Extending an earlier treatment by Kabalnov et al(Colloids and Surfaces, 24,(1987), 19-32), we derive a general condition on the mean initial droplet volume which ensures stability, even when arbitrary polydispersity is present in both size and composition of the initial droplets. We distinguish "nucleated" coarsening, which requires either fluctuations about the mean field equations or a tail in the initial droplet size distribution, from "spinodal" coarsening in which a typical droplet is locally unstable. A weaker condition for stability, previously suggested by Kabalnov et al., is sufficient only to prevent "spinodal" coarsening and is best viewed as a condition for metastability. The coarsening of unstable emulsions is considered, and shown at long times to resemble that of ordinary emulsions (with no trapped species), but with a reduced value of the initial volume fraction of dispersed phase. We discuss the physical principles relevant to the stability of emulsions with trapped species, describing how these may be exploited to restabilise partially coarsened emulsions and to "shrink" previously formed emulsion droplets to form "miniemulsions".

cond-mat.soft↗